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Products in the category of -manifolds
Authors:Andrew Bruce  Norbert Poncin
Institution:1. University of Luxembourg, Mathematics Research Unit, 4364 Esch-sur-Alzette, Luxembourg;2. University of Luxembourg, Mathematics Research Unit, 4364 Esch-sur-Alzette, Luxembourg norbert.poncin@uni.lu
Abstract:We prove that the category of /></span>-manifolds has all finite products. Further, we show that a <span class= /></span>-manifold (resp., a <span class= /></span>-morphism) can be reconstructed from its algebra of global <span class= /></span>-functions (resp., from its algebra morphism between global <span class= /></span>-function algebras). These results are of importance in the study of <span class= /></span> Lie groups. The investigation is all the more challenging, since the completed tensor product of the structure sheafs of two <span class= /></span>-manifolds is not a sheaf. We rely on a number of results on (pre)sheaves of topological algebras, which we establish in the appendix.</td> </tr> <tr> <td align=
Keywords:v026  i03/14029251  2019  1613051/20190509/images/medium/tnmp_a_1613051_ilg0001  gif" alt=" />-geometry  finite categorical product  product morphism  sheafification  locally convex topological algebra  completed tensor product
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